GREENVILLE, S.C. — At a Republican primary debate watch party in suburban Charleston last week, there was something missing: any sign of support for home-state Sen. Lindsey Graham.

Graham, the well-known national security hawk, was relegated to an earlier panel for lower-profile presidential candidates that he came to call the "happy hour" debate" by the rules set by Fox News, so perhaps the absence of supporters with buttons and bumper stickers was not surprising.

But, it also spoke to something else: Graham's willingness to cut deals with Democrats on taxes and spending to avoid defense cuts, his support for the "gang of eight" immigration plan and argument against a government shutdown standoff over funding Planned Parenthood might make him a better fit with traditional presidential primary voters in a place like New Hampshire.

"New Hampshire should be a good state for me," Graham told CQ Roll Call while walking out of a Greenville community center that was the site of a town hall meeting. "We're trying to talk about my qualifications for being commander-in-chief. We're talking about solving problems in a bipartisan fashion. I think that fits New Hampshire pretty well, and Iowa — there's a pretty big veterans community out there, so we'll how well we do in Iowa, but I've got a really good team."

Sen. John McCain, R-Ariz., Graham's close friend and political ally, won the Granite State primary twice, including 2008 on his way to the GOP nomination. And Graham must be hoping that despite his minuscule poll numbers (He got 1 percent there in a new Franklin Pierce University-Boston Herald survey .), enough McCain voters will come on board and support the campaign of Arizonan's "illegitimate son."

Graham's polling at 2 percent in Iowa, according to a CNN/ORC poll released Wednesday.

"It's the early state primaries that are the way forward for me, not national polling," Graham told CQ Roll Call.

Speaking after the debate, Charleston County GOP Chairman Larry Kobrovsky said he thought the earlier contests would affect the credibility of the Graham bid in South Carolina, which on the GOP side comes after Iowa and New Hampshire.

"My job as chairman is not to take any sides, but I think it's fair to say how he does in Iowa and New Hampshire will determine what happens here with that," Kobrovsky told CQ Roll Call. "You know, I think that if he's — we saw the enthusiasm for some of the candidates, I think when people look for a president he's part of that."

"I think New Hampshire and Iowa will determine how he does here, because people want somebody who's going to be our next president who can win," Kobrovsky said. Graham's holding a series of "No Nukes for Iran" meetings across the country, trying to put the focus on foreign affairs, having already been joined in the effort by McCain and former Sen. Joseph I. Lieberman, I-Conn. Monday afternoon at the event in Greenville, Graham was solo, and he drew a crowd of only a few dozen South Carolinians.

He's on a foreign policy-focused trip through his home state this week.

One of the senators most accessible to the media and most comfortable on television, Graham told reporters after the event that he planned to up his game by, in effect, being himself and being more aggressive about pushing his foreign policy views, including his call for putting as many as 10,000 U.S. ground forces fighting the Islamic State in Syria.

Polls show national security as the No. 2 issue behind the economy among voters.

"The next time we have the debate is just to be more direct. It is not enough to criticize Obama. You're not going to win this war from the air. What would you do, and how would you do it? We owe that to the American people, to the Republican party, to define who is best qualified to be commander-in-chief," Graham said.

On Wednesday, Graham showed a sign of what's to come in calling a foreign policy speech that former Florida Gov. Jeb Bush gave Tuesday evening "woefully inadequate when it comes to the U.S. ground component needed to destroy ISIL."

"It is disappointing that the president and so many candidates running for the office are unwilling to take these necessary and bold steps before it is too late. In my view, those reluctant to call for boots on the ground — the only strategy that ensures a stable Middle East and a secure America — are not prepared to be Commander-in-Chief," he said in a statement.

In the interview with CQ Roll Call a few minutes after Monday's event to drum up opposition to the international agreement with Iran regarding its nuclear program, Graham lamented that the presence of businessman Donald Trump has been "sucking all the oxygen."

"We're just all floored. Nobody saw this coming," Graham said. "Here's the problem: We've got problems with Hispanic voters and women. If you listen to Mr. Trump and some things said in that debate, we got harder right on immigration, I think we're getting real edgy on the abortion issue. I'm very pro-life, but you know you've got to understand that some exceptions make sense, at least they do for me."